department of physics and astronomy ...the ecg, mcg, or ecg-mcg inverse problem. what role do silent...
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![Page 1: DEPARTMENT OF PHYSICS AND ASTRONOMY ...the ECG, MCG, or ECG-MCG inverse problem. What role do Silent Sources play? LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT](https://reader035.vdocument.in/reader035/viewer/2022063014/5fd01392956bc716bf4922ee/html5/thumbnails/1.jpg)
LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
1
The Magnetocardiogram, Tissue Anistropy, and the
Cardiac Bidomain John Wikswo
Franz Baudenbacher Living State Physics Group
Vanderbilt University Nashville, TN 37235 USA
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
2
The First Clinical VMCG
Machine Vector
Magnetocardiography Stanford ~1974
1 meter
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
3
Questions Regarding the MCG
Information Content? • Does the MCG contain
information not present in the ECG?
The Inverse Problem
• There is no unique solution to the ECG, MCG, or ECG-MCG inverse problem. What role do Silent Sources play?
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
4 s00021
The uniform double-layer model
• Assumes – Uniform thickness – Uniform strength – Current perpendicular
to the wave front • Dipole moment and
potential V(r) are determined by the solid angle subtended by the double-layer rim Heart vector or dipole
moment versus time
10 centimeters
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
5
LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
s0338 s0159
The electric and magnetic heart vectors
• m = ½ r x p explains relation of electric and magnetic vectors • Double-layer rim determines both m and p • Little significant new information in the MCG…?
10 centimeters
W.H. Barry, et al., Science, 198: 1159-1162 (1977);; Cardiovascular Physics, Karger, Basil, 1979, pp. 1-67.
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
6 s00397
s02734
1 millimeter: Cardiac fiber sheets
10-9 meters
104 meters
S00703
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
7
It’s the anisotropy…
Corbin and Scher, 1977
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
8
LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
s0643 s0419
Cardiac fiber orientation is the source of the new information
• Circulating current components are electrically silent • Only magnetic fields can distinguish between two possible models
10 centimeters
Wikswo and Barach, J. Theoretical Biol., 95: 721-729 (1982)
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
9 It’s the anisotropy….
3-D vs.
2-D
The cardiac syncytium: A three-dimensional non-linear anisotropic bidomain
1 millimeter
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
10
2-D Bidomain Equations • Homogenized • Coupled Vm & Ve
• Nonlinear reaction-diffusion equation
• Boundary value equation
s1350
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
11
The Cardiac Bidomain • Intra- and extracellular
spaces have unequal anisotropies in their electrical conductivities. Really? – Magnetic fields – Virtual electrodes – Quatrefoil reentry – Defibrillation?
Unit Bloc k
Intrac ellul ar
Non-linear Mem br ane
Extr ace llu lar
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
12
Recording from the Bidomain
• Extracellular potential – Extracellular electrode arrays ( <1250 )
• Intracellular potential – Intracellular microelectrodes ( < 2 )
• Membrane potential – Voltage-sensitive fluorescent dyes ( 256 – 10,000 )
• Net action currents – Scanning SQUID microscope ( 1 )
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
13
Optical Imaging of the Transmembrane Action Potential During Stimulation, Reentry, Fibrillation,
and Defibrillation • Langendorff-
perfused rabbit heart
• Voltage-sensitive dye in membrane measures Vm
• Laser illumination • High-speed
charge-coupled-device (CCD) camera
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
14 TL129 S4609
Vanderbilt cardiac imaging system Verdi diode-pumped solid-state laser Di-4-ANEPPS voltage dye Light delivered by bundles of optical fibers Dalsa CCD camera: 12 bit 64x64 pixels 1200 frames/sec 10 x 5 x 7.5 cm3 bath
37 oC Tyrode’s solution
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
15
Gus2: MATLAB
Data Viewing Program
Written by Gustavo Rohde
Four S2 frames indicated by LED
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
16
Injecting -20 mA into Equal-Anisotropy Cardiac Tissue
• Point cathodal stimulation
• Virtual cathode depolarizes (red)
• Wave front propagates from the edge of the virtual cathode (yellow)
Fiber Direction
7.5 mm
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
17 s0704 s1325
Bidomain Anisotropy
σix 0.2 S/m σiy 0.02 S/m
σex 0.8 S/m
σey 0.2 S/m
σix / σiy = 10
σex / σey = 4
There is no single coordinate system in which the tensor conductivity is everywhere diagonal!
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
18
Virtual electrodes in cardiac tissue • As a result of unequal
electrical anisotropies in intracellular and extracellular spaces:
• Point cathodal stimulation
• Virtual cathode depolarizes (red)
• Virtual anodes hyperpolarize (blue)
Wikswo, Lin and Abbas. Biophys. J. 69 :2195-2210, 1995
7.5 mm
1 millimeter
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
19
Puzzle Four modes of stimulating cardiac tissue
• Cathode make (turn on negative current) • Anode make (turn on positive current) • Cathode break (turn off long negative current) • Anode break (turn off long positive current)
Dekker, E. "Direct current make and break thresholds for pacemaker electrodes on the canine ventricle." Circ Res, 27:811, 1970
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
20
0 ms 2 4 6 8
0 ms 3 6 9 12
0 ms 2 4 6 8
1 mm
0 ms 3 6 9 12
Cathode Make
-10 mA
Anode Make +10 mA
Cathode Break
-2 mA
Anode Break +3mA
Depolarized
Hyperpolarized
<-2 -1 0 1
>2
∆F/F (%)
Fiber Direction
--- Virtual Electrodes ---
Wikswo, Lin and Abbas. Biophys. J. 69 :2195-2210, 1995
.
10,000 pixel/frame
TL129 S4614
Synchronous Imaging of Point Activation Patterns
1 millimeter
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Optical imaging of quatrefoil reentry Transmembrane potential distributions from selected frames of a movie for cathodal-break stimulation
Cathodal-Break Isochrones Anodal-Break Isochrones 22 68 11
3
135 90 45 126
Vm_expt.mpg
1 millimeter
Courtesy of Marc Lin Lin, Roth, and Wikswo, J. Cardiovasc. Electrophysiol., 10: 574-586 (1999)
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
22
It’s the anisotropy…
Corbin and Scher, 1977
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
23
Magnetic Field From a Circular Action LV Free
Wall Action Potential:
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
s1157 s1151
The Apex Will Have a Complicated B Field
10 centimeters
Roth and Wikswo, Biophys. J., 50: 739-745 (1986)
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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SQUID Magnetometers
• Superconducting • QUantum • Interference • Device
• Bandwidth: DC-10 kHz • Image net action current in x-y plane • Big, smaller, smallest…
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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NanoSQUID: Cooled with liquid N2 and liquid He ……
Bellows Mechanism
Vacuum Port
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
27
The SQUID lives in the vacuum space …
25µm Sapphire Window
Lever Mechanism
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
28
Wind a Pickup Coil ….
25µm Nb Wire
Sapphire Bobbin
250 – 500µm
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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In Reality ..
SQUID
Pickup Coil
He-Reservoir
77K -Radiation Shield
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Pickup Coil
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
31
Image the LV Free Wall ...
•Scanning SQUID microscope •Isolated rabbit heart •Point stimulation •Anisotropy should produce a quatrefoil current pattern
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Langendorff-Perfused Isolated Rabbit Heart
Bath 15µm Mylar-Foil
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Isolated Rabbit Heart
Dewar Tail
From Heat Exchanger
To Heat Exchanger
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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MCG From the LV Free Wall
16 mm
16 mm
Scan Area
Pixel size 0.16 mm2
Bandwidth = 1 kHz
B-FMPR
0 100 200 300 400 500
-800
-600
-400
-200
0
200
400
600
Mag
netic
Fie
ld [p
T]
Time [ms]
1 pT ~ Bearth/100,000,000
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
35
Cathodal Current Injection Followed by Initiation of Action Currents
1 ms after Stimulus
[mm]
Stimulus: 5 ms, 1.5 mA
Fiber Direction
nT
[mm
]
1 cm
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Layered Bidomain Model
Experiment
nT pT
Pickup Coil
B-FMPR Stimulus
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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Propagation of Action Currents
4 ms 10 ms 16 ms
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LIVING STATE PHYSICS GROUP DEPARTMENT OF PHYSICS AND ASTRONOMY, VANDERBILT UNIVERSITY
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The Magnetic Field From Action Currents in Isolated Cardiac Tissue – The Apex
S00835A
Near_apex.mpg
Stimulus 0.6 mA 5 ms
2 ms 3 ms 4 ms
5 ms 6 ms 8 ms
Courtesy of Franz Baudenbacher
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Forthcoming…
• Measured magnetic field gives current • Measured Vm gives the voltage • Model of both requires the bidomain
conductivities (Eason and Trayanova)
• Obtain the doubly anisotropic bidomain conductivities by fitting the model to the data
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S2- Point Stimulation
0 100 200 300 400 500 600 7000
50
100
150
200
250
300
350
400
450
[ms]
[arb
it un
its]
6 ms
12 ms
18 ms
Point Electrode
S2-S1=240 ms
S = 6*Threshold
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20 40 60 80 100 120
20
40
60
80
100
120
Vm Isochrones – LV Free Wall
Point Stimulation
Fiber Orientation
ventricle_propagation.mpg
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20 40 60 80 100 120
20
40
60
80
100
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Vm Isochrones - Apex
Point Stimulation
apex_propagation.mpg
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Velocities as a function of direction
0 50 100 150 200 250 300 3504
6
8
10
12
14
16
18
20
22
24
angle [deg]
Pro
paga
tion
velo
city
[ar
bit.
uni
ts]
ventricleapex
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SQUID Senses Spatial Vm Gradients Repolarization Injury Currents
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Gradients in Repolarization
0 500 1000 1500-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05Magneto Cardio Gram
pixel (14,5)pixel (20,5)
repolarization.mpg
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Dipole Signature in ST-segment
pT
71 ms
b-frpo.mpg
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Information Content of the MCG • Evidence that electrically silent sources exist.
• Magnetic mapping can provide images of net action current in cardiac tissue.
• Combined electric and magnetic measurements can provide the anisotropic conductivities and the non-linear membrane properties.
• A dimensional biodomain model combined with a realistic fiber architecture may provide a better understanding of the MCG.
• MCG allows probing of gradients in repolarization and resting potentials (injury currents).
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Acknowledgements
Rashi Abbas Petra Baudenbacher
J. J. Koola Joe Kirschvink Jenny Holzer
Luis Fong
Marc Lin Nick Peters
Scott Renkes Brad Roth
Zvonko Trontelj Ben Weiss
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Vanderbilt University
Living State Physics Group